Saturday, 7 January 2017

Few, if any, have contributed as much to game theory as Thomas Schelling. Or, to perhaps be more accurate, surely nobody has more powerfully shown the value of applying game theory to understand the world around us. As we reflect on Schelling's contribution to knowledge, following his death in December, I think it is particularly useful to look back on one of his less touted but fundamental observations - conflict is rarely a zero-sum game.

To put Schelling's insight in perspective it is important to recognise that the early development of game theory was hugely influenced by zero-sum games. These are games in which total payoffs always sum to zero meaning that one player's gain must be another player's loss. Sporting and parlour games, like chess and bridge, are naturally modelled as zero-sum because they are about winning and losing. Zero-sum games also have some nice theoretical properties which mean they are particularly amenable to analysis. For this latter reason, more than any other, by the 1950's game theory was increasingly becoming the study of zero-sum games.

On the strategy of pure conflict - the zero sum games - game theory has yielded important insight and advice. But on the strategy of action where conflict is mixed with mutual dependence - the non-zero-sum games involved in wars and threats of war, strikes, negotiations, criminal deterrence, class war, race war, price war, and blackmail; manoeuvring in a bureaucracy or in a social hierarchy or in a traffic jam; and the coercion of one's own children - traditional game-theory has not yielded comparable insight or advice.

Game theory, therefore, needed to reorient itself away from zero-sum games. A fundamental part of the argument, clear in the range of examples Schelling gave in the quote above, is that most conflict is not zero-sum.
One of the main examples Schelling used was the cold war. The U.S. and Soviet Union were clearly in extreme conflict. But that does not mean there was not scope for mutual gain. Comparing two possible scenarios easily illustrates the point. Scenario 1: The U.S. and Soviets throw nuclear weapons at each other causing mass devastation and millions of civilian casualties. Scenario 2: The U.S. and Soviets don't fire any nuclear weapons and there are no civilian casualties. Clearly, scenario 2 is considerably better for both the U.S. and Soviets than scenario 1.
As this example illustrates, conflict does not preclude potential gains from 'coordinating' or 'cooperating' on a mutually beneficial outcome - in this case avoiding nuclear war. Or, to quote Schelling:

These are games in which, though the element of conflict provides the dramatic interest, mutual dependence is part of the logical structure and demands some kind of collaboration or mutual accommodation - tacit, if not explicit - even if only in the avoidance of mutual disaster.

I particularly like the allusion to 'conflict provides the dramatic interest'. With that in mind let us look at Brexit and Trump.
Brexit is a conflict between the U.K. and E.U. and is clearly not zero-sum. If trade negotiations go badly then both will suffer. If they go well then disaster can be averted. The popular press, and Brexiters, seem, however, to prefer to portray the conflict as zero-sum. Particularly telling are the arguments over whether the U.K. government should give details of its key negotiating demands. The government argues that showing its hand would weaken its bargaining position. Nonsense. This is a logic based on a zero-sum conflict like bridge, not a negotiation where mutual accommodation is essential. To quote Schelling again:

These are also games in which, though secrecy may play a strategic role, there is some essential need for the signalling of intentions and the meeting of minds.

In truth, I think the government plays along with the zero-sum narrative because it provides a convenient shield to hide the fact they don't have a plan. It is, though, interesting to see how easily the public buys the narrative.
And so to Trump, where just about every conflict is portrayed as zero-sum. Trade with China is a zero-sum game, as is immigration from Mexico, climate change, and so on. Clearly, none of these issues are remotely zero-sum. Again, however, a narrative of pure conflict seems to go down well with a large proportion of the public. Possibly because it is easier to get excited about someone who will 'defend your interests against the enemy' rather than 'negotiate a mutually beneficial compromise'.
Looking back, there is no doubt that Schelling's call for a reorientation of game theory had an effect. Today, zero-sum games are considered by game theorists to be the theoretical extreme case that Schelling argued they were. It is much more likely that the prisoners dilemma or ultimatum game get the attention. Outside of academic circles, however, it would seem that Schelling's critical insight remains poorly understood. Many seemingly prefer to view conflict as zero-sum. Hopefully, we can still avert disaster.